סאִיז דָאךְ אַלְץ הֶבֶל הַבָלִים, אֵין עוד מִלְבַדו
"This is all fleeting and transient, there is nothing but Him(Hashem)!" ("Hevel Havalim" is found a few times in Koheles-1:2 and 12:8. "Ein Od Milvado" is found in Devarim-4:35)
Rav Shimshon Pincus ZT"L, in his sefer Shabbos Malchusa, speaks of a very meaningful concept; When someone is so overcome with emotion, to the point where no words would suffice to describe what he or she is feeling, one just breaks out in song. This, he states, is why we sing as we welcome in the Holy Shabbos, or more specifically, why we sing certain verses in 'Lecha Dodi' pertaining to Yemos Hamashiach (Days of the Final Redemption). Just as we may prepare all we can for The Redemption to come, and once it does come it will be so beyond anything we could have anticipated, so too by Shabbos-we go through the mundane week, preparing for the Kedusha (Holiness) of Shabbos, but once it arrives, we see how we could have never anticipated such an elevated state of existance that is the Kedusha of Shabbos. We are speechless. This is why, at that point on friday night, we break out in song.
What does this vort have to do with the song above you may ask? Well, after the words in this niggun there's a 'nay nay nay' type of chant that we sing (hopefully I'll have a clip so you could hear it). So, I would like to submit, that here too the 'nay nay nay' is representing our "breaking out in song." I've spoken before about the concept of recognizing the existance of a Borei Olam (Creator of the Universe) in all His Glory bringing an individual an unbelievable level of simcha (happiness). For such a simcha, there are no words. All we can do is break out in song. "...There is nothing but Him!!-Nay nay nay nay nay...!"